The<tex>$p$</tex>-Sphere Encoder: Peak-Power Reduction by Lattice Precoding for the MIMO Gaussian Broadcast Channel

A vector precoding scheme has been recently proposed for the multiple-input multiple-output (MIMO) Gaussian broadcast channel. This technique minimizes the instantaneous transmitted power of linearly precoded signals, but does not take into account the peak-to-average-power ratio (PAPR). In this paper, we present a modified vector precoding scheme where a perturbation vector is chosen in order to take into account both the instantaneous power and the instantaneous peak power of the transmitted signal. This is obtained by minimizing the $rho$ -norm of the transmitted signal, for $rhogeq 2$ . For this reason, the scheme is referred to as the $rho$ -sphere encoder. We demonstrate the performance of the proposed scheme applied to a MIMO i.i.d. Rayleigh fading downlink channel with simple channel inversion. We show that by choosing $rhogeq 2$ , the proposed $rho$ -sphere encoder yields a tradeoff between power efficiency, PAPR reduction, and complexity. In particular, with eight antennas, the proposed algorithm significantly reduces the tail of the PAPR distribution with very small degradation terms of bit-error rate with respect to standard vector precoding.